Hajime Togashi

Variational study for the equation of state of asymmetric nuclear matter at finite temperatures

Abstract An equation of state (EOS) for uniform asymmetric nuclear matter (ANM) is constructed at zero and finite temperatures by the variational method starting from the nuclear Hamiltonian that is composed of the Argonne v18 and Urbana IX potentials. At zero temperature, the two-body energy is calculated with the Jastrow wave function in the two-body cluster approximation which is supplemented by Mayerʼs condition and the healing-distance condition so as to reproduce the result by Akmal, Pandharipande and Ravenhall. The energy caused by the three-body force is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation conditions. The masses and radii of neutron stars obtained with the EOS are consistent with recent observational data. At finite temperatures, thermodynamic quantities such as free energy, internal energy, entropy, pressure and chemical potentials are calculated with an extension of the method by Schmidt and Pandharipande. The validity of the frozen-correlation approximation employed in this work is confirmed as compared with the result of the fully minimized calculation. The quadratic proton-fraction-dependence of the energy of ANM is confirmed at zero temperature, whereas the free energy of ANM deviates from the quadratic proton-fraction-dependence markedly at finite temperatures. The obtained EOS of ANM will be an important ingredient of a new nuclear EOS for supernova numerical simulations.

Nuclear equation of state for core-collapse supernova simulations with realistic nuclear forces

Abstract A new table of the nuclear equation of state (EOS) based on realistic nuclear potentials is constructed for core-collapse supernova numerical simulations. Adopting the EOS of uniform nuclear matter constructed by two of the present authors with the cluster variational method starting from the Argonne v18 and Urbana IX nuclear potentials, the Thomas–Fermi calculation is performed to obtain the minimized free energy of a Wigner–Seitz cell in non-uniform nuclear matter. As a preparation for the Thomas–Fermi calculation, the EOS of uniform nuclear matter is modified so as to remove the effects of deuteron cluster formation in uniform matter at low densities. Mixing of alpha particles is also taken into account following the procedure used by Shen et al. (1998, 2011). The critical densities with respect to the phase transition from non-uniform to uniform phase with the present EOS are slightly higher than those with the Shen EOS at small proton fractions. The critical temperature with respect to the liquid–gas phase transition decreases with the proton fraction in a more gradual manner than in the Shen EOS. Furthermore, the mass and proton numbers of nuclides appearing in non-uniform nuclear matter with small proton fractions are larger than those of the Shen EOS. These results are consequences of the fact that the density derivative coefficient of the symmetry energy of our EOS is smaller than that of the Shen EOS.

Application of the nuclear equation of state obtained by the variational method to core-collapse supernovae

The equation of state (EOS) for hot asymmetric nuclear matter which is constructed with the variational method starting from the Argonne v18 and Urbana IX nuclear forces is applied to spherically symmetric core-collapse supernovae (SNe). We first investigate the EOS of isentropic beta-stable SN matter, and find that the matter with the variational EOS is more neutron-rich than that with the Shen EOS. Using the variational EOS for uniform matter supplemented by the Shen EOS of non-uniform matter at low densities, we perform general-relativistic spherically symmetric simulations of core-collapse SNe with and without neutrino transfer, starting from a presupernova model of 15 solar mass. In the adiabatic simulation without neutrino transfer, the explosion is successful, and the explosion energy with the variational EOS is larger than that with the Shen EOS. In the case of the simulation with neutrino transfer, the shock wave stalls and then the explosion fails, as in other spherically symmetric simulations. The inner core with the variational EOS is more compact than that with the Shen EOS, due to the relative softness of the variational EOS. This implies that the variational EOS is more advantageous for SN explosions than the Shen EOS.

Equation of state for neutron stars with hyperons using a variational method

We investigate the effects of the odd-state part of bare

A new equation of state for core-collapse supernovae based on realistic nuclear forces and including a full nuclear ensemble

\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Lambda}}

Cluster variational method for nuclear matter with the three-body force

interactions on the structure of neutron stars (NSs) by constructing equations of state (EOSs) for uniform nuclear matter containing

Heavy nuclei as thermal insulation for protoneutron stars

\mathrm{\ensuremath{\Lambda}}

Nuclear equation of state for core-collapse supernovae with realistic nuclear forces

and

Nuclear equation of state with the variational method and its application to supernova simulations

{\mathrm{\ensuremath{\Sigma}}}^{\ensuremath{-}}

Equation of state for nuclear matter in core-collapse supernovae by the variational method

hyperons with use of the cluster variational method. The isoscalar part of the Argonne v18 two-nucleon potential and the Urbana IX three-nucleon potential are employed as the interactions between nucleons, whereas, as the bare